Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T00:16:07.862Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the normalised moments of distributions with non-monotonic hazard rate

Published online by Cambridge University Press:  14 July 2016

H. L. MacGillivray
H. L. MacGillivray*
Affiliation:
University of Queensland
*
∗Postal address: Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067, Australia.
Get access Rights & Permissions [Opens in a new window]

Abstract

For distributions of non-negative random variables with a monotonic hazard rate, it is well known that the normalised moments have the same sign-regular property as the distribution. This note extends this correspondence in properties for some common distributions with non-monotonic hazard rates, linking a change in sign-regular properties.

Keywords

HAZARD RATEVARIATION-DIMINISHING THEOREMSNORMALISED MOMENTSSIGN-REGULARITYPARTICLE-SIZE DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 530 - 535
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E., Marshall, A. W. and Proschan, F. (1963) Properties of probability distributions with monotone hazard rate. Ann. Math. Statist. 34, 375–389.Google Scholar
Karlin, S. (1968) Total Positivity, Vol. I. Stanford University Press.Google Scholar
Karlin, S., Proschan, F. and Barlow, R. E. (1961) Moment inequalities of Pólya frequency functions. Pacific J. Math. 11, 1023–1033.Google Scholar
Macgillivray, H. L. (1980) The moment ratios of particle size distributions in some simple growth models. J. Appl. Prob. 17, 956–967.Google Scholar